measurable function

b) If a functions codomain is a topological space and the functions domain is a measurable space, then the function is measurable if the inverse image of every open set in its codomain is a measurable set in its domain.
Wikipedia foundation.
Look at other dictionaries:
Measurable function — In mathematics, particularly in measure theory, measurable functions are structure preserving functions between measurable spaces; as such, they form a natural context for the theory of integration. Specifically, a function between measurable… … Wikipedia
Weakly measurable function — See also= In mathematics mdash; specifically, in functional analysis mdash; a weakly measurable function taking values in a Banach space is a function whose composition with any element of the dual space is a measurable function in the usual… … Wikipedia
Measurable cardinal — In mathematics, a measurable cardinal is a certain kind of large cardinal number. Contents 1 Measurable 2 Real valued measurable 3 See also 4 References … Wikipedia
Simple function — In mathematical field of real analysis, a simple function is a real valued function over a subset of the real line which attains only a finite number of values. Some authors also require simple functions to be measurable; as used in practice,… … Wikipedia
Probability density function — Boxplot and probability density function of a normal distribution N(0, σ2). In probability theory, a probability density function (pdf), or density of a continuous random variable is a function that describes the relative likelihood for this… … Wikipedia
Characterizations of the exponential function — In mathematics, the exponential function can be characterized in many ways. The following characterizations (definitions) are most common. This article discusses why each characterization makes sense, and why the characterizations are independent … Wikipedia
Integrable function — In mathematics, an integrable function is a function whose integral exists. Unless specifically stated, the integral in question is usually the Lebesgue integral. Otherwise, one can say that the function is Riemann integrable (i.e., its Riemann… … Wikipedia
Convex function — on an interval. A function (in black) is convex if and only i … Wikipedia
Weight function — A weight function is a mathematical device used when performing a sum, integral, or average in order to give some elements more weight or influence on the result than other elements in the same set. They occur frequently in statistics and… … Wikipedia
Locally integrable function — In mathematics, a locally integrable function is a function which is integrable on any compact set of its domain of definition. Formal definition Formally, let Omega be an open set in the Euclidean space scriptstylemathbb{R}^n and scriptstyle… … Wikipedia